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arXiv · 1809.07226

Critical parameters for reaction-diffusion equations involving space-time fractional derivatives

Sunday A. Asogwa·Mohammud Foondun·Jebessa B. Milena·Erkan Nane
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Abstract

We will look at reaction-diffusion type equations of the following type, $$\partial^β_tV(t,x)=-(-Δ)^{α/2} V(t,x)+I^{1-β}_t[V(t,x)^{1+η}].$$ We first study the equation on the whole space by making sense of it via an integral equation. Roughly speaking, we will show that when $0<η\leqη_c$, there is no global solution other than the trivial one while for $η>η_c$, non-trivial global solutions do exist. We also study the equation on a bounded domain with Dirichlet boundary condition and show that the presence of the time derivative induces a significant change in the behaviour of the solution.

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Sunday A. Asogwa, Mohammud Foondun, Jebessa B. Milena, Erkan Nane. 2018-09-19. Critical parameters for reaction-diffusion equations involving space-time fractional derivatives. https://arxiv.org/abs/1809.07226

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